I killed a buzzing thing

I killed a buzzing thing. It was mortally wounded and flying in little circles on the surface of the table, so I felt I had to put it out of its misery, but I don't want to kill anything. OK, buzzing things about a millimetre across feel like they don't count, but illogically being about a centimetre feels over some threshold.

Maybe my career as a vampire slayer is not ordained. Though I don't know, vampires known to be evil come in the same category as plague-carrying mosquitoes, "Sorry bub, but its you or me."

Bridge

*Last* time I played bridge it was all 4443, 4443, 4432, 4443, 4443, every hand making me go "OK, now how do you bid to an uncontested partial score again?"

*This* time, 55s and 67s and other crazy shit singleton beer cards[1] abounded. I arrived to witness J play four consecutive hands, the last three with 4-0 or 5-0 trump splits against. *Several* hands with no notable feature other than a spade straight[1]. But it was fun and instructive, as always.

[1] The beer card is the 7 of diamonds. A spade straight is 356789 or similar. Neither has any importance for the play of the game, except if you find your life insufficiently illuminated by bidding conventions.

Dice update

1. You could eliminate the rolling problem on a d7 by using a sphere and painting seven equal areas on the surface (in an appropriately semi-symmetric non-striped way). The only flaw being it not ending on one certain face.

2. You could do that, but have a heptahedral die with little airbags that expands into a sphere for rolling, and then you collapse remotely causing it to fall on one face. But that's over-engineered.

3. ptc suggests the question with the d0 is you're looking at external faces, which should be the only ones that count. If you have a gigantic cube surrounding the earth, that could be a d0. Though rolling it is dangerous.

4. What is the generalisation of a dn for n not positive? Consider Euler's formula. Define D=2+E-V, where E=number of edges and V=number of vertices. For simply connected solids, eg. polyhedrons, D=F. Aha, we're onto a concept we can generalise. For D is also defined for other shapes†. A torus divided into n has D=n+2 which isn't very helpful‡. However, two spheres with n total regions has D=n-2.

So if n is two, (eg. Each sphere consists of a single vertex and single face, and no edges -- I think this isn't pathological by euler characteristic standards), D=0 as desired.

Except this isn't very vivid. I can show you two marbles and say "Lo! These two marbles are a no-sided die" and probably be a hit at Buddhist drug raves, but it doesn't actually illuminate the problem very helpfully, or suggest interesting further maths/engineering to do :)

† Use the Euler Characteristic, explanations tomorrow. In short, V-E+F=Chi, where Chi is defined topologically. Polyhedrons are all topologically equivalent to a sphere, and Chi is two. Donuts and holed solids have Chi=2-2g where g is the genus is number of holes. Two spheres have Chi=4, as you can see by adding up V, E, F and getting 2 for each.

‡ Except maybe to act as a warning bell that our generalisation may be starting to come apart at the seams already. In what sense is a torus havign seven regions equivalent to a d9?